On a transmission eigenvalue problem for a spherically stratified coated dielectric

David  Colton; Yuk-J.  Leung

doi:10.3934/ipi.2016004

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2016, Volume 10, Issue 2: 369-378. Doi: 10.3934/ipi.2016004

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On a transmission eigenvalue problem for a spherically stratified coated dielectric

David Colton^1, and
Yuk-J. Leung^1,

1.
Department of Mathematical Sciences, University of Delaware, Newark, Delaware 19716-2553

Received: June 30, 2015

Published: April 2016

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Abstract

Suppose that the boundary of the unit ball in $R^3$ is coated with a very thin layer of a highly conductive material and the refractive index $n(x)$ inside the ball is spherically stratified. We show that in this case the set of transmission eigenvalues behave quite differently than in the previous studied case of an uncoated ball. In particular, if the index of refraction varies smoothly across the boundary of the unit ball we show that complex eigenvalues always exist and accumulate on the real axis and that the real and complex eigenvalues uniquely determine the index of refraction without any restriction on its magnitude.

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Mathematics Subject Classification: Primary: 30D15, 34B09, 34B24, 35Q60.

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